Hi Tom,
Yes this is strange. I have not used Offset in this way. I have used it countless times to do a simple offset of a surface (or quilt) and have also used it to replace a surface (but quite a while back so do not really remember it).
Essentially I found I did not understand how the other two choices in Offset worked so I did not use them.
In the example case you show it makes a solid feature but does not recognise the intersection with the other leg of the solid. It is as if it has made a surface feature but filled it from below with the surface boundary remaining in the other solid as it would if it was surface only. This is M060
As a complete change of tack how about a projected curve as the base of your weld and a sweep (for me VSS) to give the inclined wall and then use solidify? Very robust. If you are really keen you can copy the surfaces of the tube and the block then merge these to your sweep to get a surface volume which you then solidify but unless you need this volume for something it may be over the top.
Regards, Brent.